Generalization of a theorem of Gonchar

Let $X, Y$ be two complex manifolds, let $D\subset X,$ $G\subset Y$ be two nonempty open sets, let $A$ (resp. $B$) be an open subset of $\partial D$ (resp. $\partial G$), and let $W$ be the 2-fold cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ Under a geometric condition on the boundary sets $A$ and $B,$ we show that every function locally bounded, separately continuous on $W,$ continuous on $A\times B,$ and separately holomorphic on $(A\times G) \cup (D\times B)$ "extends" to a function continuous on a "domain of holomorphy" $\hat{W}$ and holomorphic on the interior of $\hat{W}.$Comment: 14 pages, to appear in Arkiv for Matemati

Numerical Modeling of Dependent Credit Rating Transitions with Asynchronously Moving Industries

Two models of dependent credit rating migrations governed by industry-specific Markovian matrices, are considered. Caused by macroeconomic factors, positive and negative unobserved tendencies, encoded as values "1" or "0" of the corresponding variables, modify the transition probabilities and render the evolutions dependent. They are neither synchronized across industry sectors, nor over credit classes: an upswing in some of them can coexist with a decline of the rest. The models are tested on Standard and Poor's data. MATLAB optimization software and maximum likelihood estimators are used. Obtained distributions of the hidden variables demonstrate that the considered industries migrate asynchronously trough credit classes. Since downgrading probabilities are less affected by the unobserved tendencies, estimated by Monte-Carlo simulations distributions of defaults, exhibit lighter, than for the known coupling models, tails for schemes with asynchronously moving industries. Moreover, the lightest tails were obtained in the case of industry-specific transition matrices

Exhausting domains of the symmetrized bidisc

We show that the symmetrized bidisc may be exhausted by strongly linearly convex domains. It shows in particular the existence of a strongly linearly convex domain that cannot be exhausted by domains biholomorphic to convex ones.Comment: 6 page

Quantification of Loss of Access to Critical Services during Floods in Greater Jakarta: Integrating Social, Geospatial, and Network Perspectives

This work presents a framework for assessing the socio-physical disruption of critical infrastructure accessibility using the example of Greater Jakarta, a metropolitan area of the Indonesian city. The first pillar of the framework is damage quantification based on the real flood event in 2020. Within this pillar, the system network statistics before and shortly after the flood were compared. The results showed that the flood impeded access to facilities, distorted transport connectivity, and increased system vulnerability. Poverty was found to be negatively associated with surface elevation, suggesting that urbanization of flood-prone areas has occurred. The second pillar was a flood simulation. Our simulations identified the locations and clusters that are more vulnerable to the loss of access during floods, and the entire framework can be applied to other cities and urban areas globally and adapted to account for different disasters that physically affect urban infrastructure. This work demonstrated the feasibility of damage quantification and vulnerability assessment relying solely on open and publicly available data and tools. The framework, which uses satellite data on the occurrence of floods made available by space agencies in a timely manner, will allow for rapid ex post investigation of the socio-physical consequences of disasters. It will save resources, as the analysis can be performed by a single person, as opposed to expensive and time-consuming ground surveys. Ex ante vulnerability assessment based on simulations will help communities, urban planners, and emergency personnel better prepare for future shocks

Oleı̆nik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit

We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term $W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast \rho$ satisfy an Oleı̆nik-type entropy condition. More precisely, under different sets of assumptions on the velocity function $V$, we prove that $W$ satisfies a one-sided Lipschitz condition and that $V'(W) W \partial_x W$ satisfies a one-sided bound, respectively. As a byproduct, we deduce that, as the exponential kernel is rescaled to converge to a Dirac delta distribution, the weak solution of the nonlocal problem converges to the unique entropy-admissible solution of the corresponding local conservation law, under the only assumption that the initial datum is essentially bounded and not necessarily of bounded variation

Bergman kernel and complex singularity exponent

We give a precise estimate of the Bergman kernel for the model domain defined by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where $F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$, in terms of the complex singularity exponent of $F$.Comment: to appear in Science in China, a special issue dedicated to Professor Zhong Tongde's 80th birthda

An ALM model for pension funds using integrated chance constraints

We discuss integrated chance constraints in their role of short-term risk constraints in a strategic ALM model for Dutch pension funds. The problem is set up as a multistage recourse model, with special attention for modeling short-term risk prompted by the development of new guidelines by the regulating authority for Dutch pension funds. The paper concludes with a numerical illustration of the importance of such short-term risk constraints

The decision rule approach to optimization under uncertainty: methodology and applications

Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naïvely partition or discretize the support of the random problem parameters are limited to small and medium-sized problems, or they require restrictive modeling assumptions (e.g., absence of recourse actions). In the last few decades, several solution techniques have been proposed that aim to alleviate the curse of dimensionality. Amongst these is the decision rule approach, which faithfully models the random process and instead approximates the feasible region of the decision problem. In this paper, we survey the major theoretical findings relating to this approach, and we investigate its potential in two applications areas

Analyzing multitarget activity landscapes using protein-ligand interaction fingerprints: interaction cliffs.

This is the original submitted version, before peer review. The final peer-reviewed version is available from ACS at http://pubs.acs.org/doi/abs/10.1021/ci500721x.Activity landscape modeling is mostly a descriptive technique that allows rationalizing continuous and discontinuous SARs. Nevertheless, the interpretation of some landscape features, especially of activity cliffs, is not straightforward. As the nature of activity cliffs depends on the ligand and the target, information regarding both should be included in the analysis. A specific way to include this information is using protein-ligand interaction fingerprints (IFPs). In this paper we report the activity landscape modeling of 507 ligand-kinase complexes (from the KLIFS database) including IFP, which facilitates the analysis and interpretation of activity cliffs. Here we introduce the structure-activity-interaction similarity (SAIS) maps that incorporate information on ligand-target contact similarity. We also introduce the concept of interaction cliffs defined as ligand-target complexes with high structural and interaction similarity but have a large potency difference of the ligands. Moreover, the information retrieved regarding the specific interaction allowed the identification of activity cliff hot spots, which help to rationalize activity cliffs from the target point of view. In general, the information provided by IFPs provides a structure-based understanding of some activity landscape features. This paper shows examples of analyses that can be carried out when IFPs are added to the activity landscape model.M-L is very grateful to CONACyT (No. 217442/312933) and the Cambridge Overseas Trust for funding. AB thanks Unilever for funding and the European Research Council for a Starting Grant (ERC-2013- StG-336159 MIXTURE). J.L.M-F. is grateful to the School of Chemistry, Department of Pharmacy of the National Autonomous University of Mexico (UNAM) for support. This work was supported by a scholarship from the Secretariat of Public Education and the Mexican government